Venture Capital Funds Size and Structure in a Directed Search Model

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I develop a theory of fund size and structure when fund managers add value to the companies they finance, but their human capital is scarce. I propose a matching model with directed search where managers span their nurturing activity over more projects, and entrepreneurs are privately informed about their projects' quality. Managers differ in the ability to scale up their human capital. I derive necessary and sufficient conditions for positive and negative assortative matching over managerial attention and project quality to emerge. Anticipating positive sorting, managers shrink fund size below the efficient level. Entry of unskilled managers feeds back into equilibrium sorting, increases returns at the top of the distribution - consistently with empirical evidence - and always results in a Pareto-improvement. This offers a new angle to think about policies encouraging entry in the venture capital industry. When extended to a dynamic setting, the model illustrates a novel advantage of closed, finite-horizon funds, which emerge in equilibrium even when they are socially undesirable: they attract the best entrepreneurs, who value the most the exclusive relation that a closed-end fund guarantees. Managers benefit from committing to a size in the first place.